Magnitude Comparison Task Research Articles

The effect of working memory load on the SNARC effect: Maybe tasks have a word to say.

We investigated the effect of working memory load on the SNARC (spatial-numerical association of response codes) effect under different number judgment tasks (parity judgment and magnitude comparison), using a novel dual task. Instead of exerting load over the whole block of number judgment trials, in this dual task, number judgment trials were inserted into each interstimulus interval of an n-back task, which served as the working memory load. We varied both load type (verbal and spatial) and amount (1-load, 2-load, and 3-load). The results indicated that the SNARC effect disappeared even under the 1-load condition for a parity judgment, regardless of the type of load. However, during the magnitude comparison task, the SNARC effect increased with increasing load amounts under spatial load conditions; under verbal load conditions, the SNARC effect decreased with increasing amounts of load, and disappeared during the 3-load task. The difference between the parity and magnitude tasks was not attributable to the interval stimuli or task switching. These findings confirm that different spatial-numerical associations for comparing numerical magnitudes and judgments of parity have different needs with respect to working memory resources.

Dancing with the SNARC: Measuring spatial-numerical associations on a digital dance mat.

According to the concept of embodied numerosity, bodily experiences influence the way in which we process numerical magnitude. The development of this influence could be anchored in the spatial ordering of numbers along a mental number line representation, which is measured by effects of spatial-numerical associations. The aim of this study was to investigate whether horizontally oriented full-body movement and visual presentation of a number line both contribute to spatial-numerical associations in children. We presented fourth-graders with 2 magnitude comparison tasks that differed in the relevance of magnitude information. In both tasks, we varied the amount of bodily movement in different response conditions (responding verbally, with a foot tap, or by jumping) and the visual presentation (items were presented with or without a number line). From the data, we calculated 2 spatial-numerical effects and expected to find the strongest effects if a full-body response was combined with a number line presentation. The 2 effects were differentially influenced by response modalities, but not presentation. The SNARC (= Spatial Numerical Association of Response Codes) effect was present in all conditions and was not influenced by our manipulations. In contrast, a new relative numerical congruity effect was influenced by the variations in responses in accordance with our hypotheses. The relative numerical congruity effect results suggest that responses involving bodily movement increase activation of spatial-numerical associations compared to verbal responses. These results are the first to demonstrate such an influence in a full-body approach in elementary schoolchildren. (PsycINFO Database Record

Spatial reference frames and SNARC

ABSTRACTIn this work, the role that spatial reference frames play in determining the spatial-numerical association of response codes (SNARC) effect is examined. Participants were instructed to generate an image of the numbers 1–9 oriented spatially in either a horizontal, vertical, or proximo-distal manner. Responses to a magnitude comparison task were then provided manually using keys located either to the left and right or at the bottom and top of a computer keyboard. For conditions in which the orientation of the generated image and the response locations were orthogonally misaligned, SNARC effects were not evident. It is argued that such results imply that alignment of the spatial reference frames associated with the responses and with the representation of numerical magnitude is a necessary condition for the elicitation of the SNARC effect.

Numerical magnitude processing impairments in genetic syndromes: a cross-syndrome comparison of Turner and 22q11.2 deletion syndromes.

Cross-syndrome comparisons offer an important window onto understanding heterogeneity in mathematical learning disabilities or dyscalculia. The present study therefore investigated symbolic numerical magnitude processing in two genetic syndromes that are both characterized by mathematical learning disabilities: Turner syndrome and 22q11.2 deletion syndrome (22q11DS). We further verified whether the phenotypic outcomes of these syndromes emerged from the same or different cognitive processes and therefore examined whether numerical impairments were related to working memory deficits, often observed in these syndromes. Participants were 24 girls with Turner syndrome, 25 children with 22q11DS and 48 well-matched typically developing control children. All children completed a symbolic numerical magnitude comparison task and four additional working memory tasks. Both groups of children with genetic syndromes showed similar impairments in symbolic numerical magnitude processing compared to typically developing controls. Importantly, in Turner syndrome, group differences in symbolic numerical magnitude processing disappeared when their difficulties in visual-spatial working memory were taken into account. In contrast, the difficulties in 22q11DS were not explained by poor visual-spatial working memory. These data suggest that different factors underlie the symbolic numerical magnitude processing impairments in both patient groups with mathematical learning disabilities and highlight the value of cross-syndrome comparisons for understanding different pathways to mathematical learning disabilities or dyscalculia.

Differences in Arithmetic Performance between Chinese and German Children Are Accompanied by Differences in Processing of Symbolic Numerical Magnitude.

Symbolic numerical magnitude processing skills are assumed to be fundamental to arithmetic learning. It is, however, still an open question whether better arithmetic skills are reflected in symbolic numerical magnitude processing skills. To address this issue, Chinese and German third graders were compared regarding their performance in arithmetic tasks and in a symbolic numerical magnitude comparison task. Chinese children performed better in the arithmetic tasks and were faster in deciding which one of two Arabic numbers was numerically larger. The group difference in symbolic numerical magnitude processing was fully mediated by the performance in arithmetic tasks. We assume that a higher degree of familiarity with arithmetic in Chinese compared to German children leads to a higher speed of retrieving symbolic numerical magnitude knowledge.

Neural representations of magnitude for natural and rational numbers

Humans have developed multiple symbolic representations for numbers, including natural numbers (positive integers) as well as rational numbers (both fractions and decimals). Despite a considerable body of behavioral and neuroimaging research, it is currently unknown whether different notations map onto a single, fully abstract, magnitude code, or whether separate representations exist for specific number types (e.g., natural versus rational) or number representations (e.g., base-10 versus fractions). We address this question by comparing brain metabolic response during a magnitude comparison task involving (on different trials) integers, decimals, and fractions. Univariate and multivariate analyses revealed that the strength and pattern of activation for fractions differed systematically, within the intraparietal sulcus, from that of both decimals and integers, while the latter two number representations appeared virtually indistinguishable. These results demonstrate that the two major notations formats for rational numbers, fractions and decimals, evoke distinct neural representations of magnitude, with decimals representations being more closely linked to those of integers than to those of magnitude-equivalent fractions. Our findings thus suggest that number representation (base-10 versus fractions) is an important organizational principle for the neural substrate underlying mathematical cognition.

Verbal-Spatial and Visuospatial Coding of the SNARC Effect: A Comparative Study in Cultures With Different Reading Directions.

Using the magnitude comparison task, the current study tested verbal-spatial and visuospatial coding accounts by comparing the spatial-numerical association of response codes effect in 30 Chinese-speaking and 60 bilingual Uighur Chinese participants. The experimental tasks were presented using Chinese words for 30 Chinese-speaking and 30 bilingual Uighur Chinese participants, while only Uighur words were presented to the remaining 30 bilingual Uighur Chinese participants. Overall, the results of the current study showed that verbal-spatial coding could be applied to the experimental task when presented using Chinese words, but visuospatial coding could be applied to the experimental task when presented using Uighur words. The findings demonstrated that spatial coding was flexible and depended upon the language context in which the experimental task was presented.

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children.

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude.

Executive function and magnitude skills in preschool children

Executive function (EF) has been highlighted as a potentially important factor for mathematical understanding. The relation has been well established in school-aged children but has been less explored at younger ages. The current study investigated the relation between EF and mathematics in preschool-aged children. Participants were 142 typically developing 3- and 4-year-olds. Controlling for verbal ability, a significant positive correlation was found between EF and general math abilities in this age group. Importantly, we further examined this relation causally by varying the EF load on a magnitude comparison task. Results suggested a developmental pattern where 3-year-olds’ performance on the magnitude comparison task was worst when EF was taxed the most. Conversely, 4-year-olds performed well on the magnitude task despite varying EF demands, suggesting that EF might play a critical role in the development of math concepts.

Electrophysiological markers of newly acquired symbolic numerical representations: the role of magnitude and ordinal information

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, (Trends in Cognitive 14(12):542–551, 2010). However, numerical symbols necessitate an understanding of both order and magnitude, therefore order likely also plays a role in learning about number. Here, we used an artificial symbol-learning paradigm to contrast learning approximate numerical magnitude with learning numerical order. Thirty-two adult participants were randomly assigned to either the magnitude training group, in which they were trained to associate novel abstract symbols with non-symbolic numerical magnitudes, or the order training group, in which they were taught the ordinal sequence of the symbols, in analogy to the count sequence. Subsequently, electroencephalographic (EEG) data were recorded while participants completed a magnitude comparison task with the newly learned symbols. Comparing these newly acquired symbols affected event related potentials (ERPs) in a way that resembled comparisons of real numerical symbols [e.g. Temple & Posner, (Proc Natl Acad Sci USA 95(13):7836–7841, 1998)]. Furthermore, these ERP effects did not differ across learning groups, suggesting that adults formed similar representations regardless of method of instruction. In turn, the current findings highlight the potential role of ordinal information in symbolic acquisition.

Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis.

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r=.302, 95% CI [.243, .361]) than for the non-symbolic (r=.241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school-aged children and for adults.

Evidence for distinct magnitude systems for symbolic and non-symbolic number

Cognitive models of magnitude representation are mostly based on the results of studies that use a magnitude comparison task. These studies show similar distance or ratio effects in symbolic (Arabic numerals) and non-symbolic (dot arrays) variants of the comparison task, suggesting a common abstract magnitude representation system for processing both symbolic and non-symbolic numerosities. Recently, however, it has been questioned whether the comparison task really indexes a magnitude representation. Alternatively, it has been hypothesized that there might be different representations of magnitude: an exact representation for symbolic magnitudes and an approximate representation for non-symbolic numerosities. To address the question whether distinct magnitude systems exist, we used an audio-visual matching paradigm in two experiments to explore the relationship between symbolic and non-symbolic magnitude processing. In Experiment 1, participants had to match visually and auditory presented numerical stimuli in different formats (digits, number words, dot arrays, tone sequences). In Experiment 2, they were instructed only to match the stimuli after processing the magnitude first. The data of our experiments show different results for non-symbolic and symbolic number and are difficult to reconcile with the existence of one abstract magnitude representation. Rather, they suggest the existence of two different systems for processing magnitude, i.e., an exact symbolic system next to an approximate non-symbolic system.

Developmental Continuity in the Link Between Sensitivity to Numerosity and Physical Size

Converging evidence suggests that representations of number, space, and other dimensions depend on a general representation of magnitude. However, it is unclear whether there exists a privileged relation between certain magnitude dimensions or if all continuous magnitudes are equivalently related. Four-year-old children and adults were tested with three magnitude comparison tasks – nonsymbolic number, line length, and luminance – to determine whether individual differences in sensitivity are stable across dimensions. A Weber fraction (w) was calculated for each participant in each stimulus dimension. For both children and adults, accuracy and w values for number and line length comparison were significantly correlated, whereas neither accuracy nor w was correlated for number and luminance comparison. However, although line length and luminance comparison performance were not correlated in children, there was a significant relation in adults. These results suggest that there is a privileged relation between number and line length that emerges early in development and that relations between other magnitude dimensions may be later constructed over the course of development.

Perceiving numbers does not cause automatic shifts of spatial attention

It is frequently assumed that the brain codes number magnitudes according to an inherent left-to-right spatial organization. In support of this hypothesis it has been reported that in humans, perceiving small numbers induces automatic shifts of attention toward the left side of space whereas perceiving large numbers automatically shifts attention to the right side of space (i.e., Attentional SNARC: Att-SNARC; Fischer, Castel, Dodd, & Pratt, 2003). Nonetheless, the Att-SNARC has been often not replicated and its reliability never tested. To ascertain whether the mere perception of numbers causes shifts of spatial attention or whether number–space interaction takes place at a different stage of cognitive processing, we re-assessed the consistency and reliability of the Att-SNARC and investigated its role in the production of SNARC effects in Parity Judgement (PJ) and Magnitude Comparison (MC) tasks. In a first study in 60 participants, we found no Att-SNARC, despite finding strong PJ- and MC-SNARC effects. No correlation was present between the Att-SNARC and the SNARC. Split-half tests showed no reliability of the Att-SNARC and high reliability of the PJ- and MC-SNARC. In a second study, we re-assessed the Att-SNARC and tested its direct influence on a MC-SNARC task with laterally presented targets. No Att-SNARC and no influence of the Att-SNARC on the MC-SNARC were found. Also in this case, the SNARC was reliable whereas the Att-SNARC task was not. Finally, in a third study we observed a significant Att-SNARC when participants were asked to recall the position occupied on a ruler by the numbers presented in each trial: however the Att-SNARC task was not reliable. These results show that perceiving numbers does not cause automatic shifts of spatial attention and that whenever present, these shifts do not modulate the SNARC. The same results suggest that numbers have no inherent mental left-to-right organization and that, whenever present, this organization can have both response-related and strategically driven memory-related origins. Nonetheless, response-related factors generate more reliable and stable spatial representations of numbers.

Task instructions determine the visuospatial and verbal-spatial nature of number-space associations.

Evidence for number-space associations comes from the spatial-numerical association of response codes (SNARC) effect, consisting in faster reaction times to small/large digits with the left/right hand, respectively. Two different proposals are commonly discussed concerning the cognitive origin of the SNARC effect: the visuospatial account and the verbal-spatial account. Recent studies have provided evidence for the relative dominance of verbal-spatial over visuospatial coding mechanisms, when both mechanisms were directly contrasted in a magnitude comparison task. However, in these studies, participants were potentially biased towards verbal-spatial number processing by task instructions based on verbal-spatial labels. To overcome this confound and to investigate whether verbal-spatial coding mechanisms are predominantly activated irrespective of task instructions, we completed the previously used paradigm by adding a spatial instruction condition. In line with earlier findings, we could confirm the predominance of verbal-spatial number coding under verbal task instructions. However, in the spatial instruction condition, both verbal-spatial and visuospatial mechanisms were activated to an equal extent. Hence, these findings clearly indicate that the cognitive origin of number-space associations does not always predominantly rely on verbal-spatial processing mechanisms, but that the spatial code associated with numbers is context dependent.

In touch with numbers: Embodied and situated effects in number magnitude comparison

The idea of embodied numerosity denotes that seemingly abstract number concepts (e.g., magnitude) are rooted in bodily experiences and situated action. In the present study we evaluated whether there is an embodied representation of the place–value structure of the Arabic number system and if so whether this representation is influenced by situated aspects. In a two-digit number magnitude comparison task participants had to directly touch the larger of two numbers. Importantly, pointing responses were systematically biased toward the decade digit of the target number. Additionally, this leftward bias towards the tens digit was reduced in unit–decade incompatible number pairs. Thereby, we demonstrated an influence of place–value processing on manual pointing movement. Our results therefore corroborate the notion of an embodied representation of the place–value structure of Arabic numbers which is modulated by situated aspects.

Toward a model framework of generalized parallel componential processing of multi-symbol numbers.

In this article, we propose and evaluate a new model framework of parallel componential multi-symbol number processing, generalizing the idea of parallel componential processing of multi-digit numbers to the case of negative numbers by considering the polarity signs similar to single digits. In a first step, we evaluated this account by defining and investigating a sign-decade compatibility effect for the comparison of positive and negative numbers, which extends the unit-decade compatibility effect in 2-digit number processing. Then, we evaluated whether the model is capable of accounting for previous findings in negative number processing. In a magnitude comparison task, in which participants had to single out the larger of 2 integers, we observed a reliable sign-decade compatibility effect with prolonged reaction times for incompatible (e.g., -97 vs. +53; in which the number with the larger decade digit has the smaller, i.e., negative polarity sign) as compared with sign-decade compatible number pairs (e.g., -53 vs. +97). Moreover, an analysis of participants' eye fixation behavior corroborated our model of parallel componential processing of multi-symbol numbers. These results are discussed in light of concurrent theoretical notions about negative number processing. On the basis of the present results, we propose a generalized integrated model framework of parallel componential multi-symbol processing.

Parietal dysfunction during number processing in children with fetal alcohol spectrum disorders.

Number processing deficits are frequently seen in children prenatally exposed to alcohol. Although the parietal lobe, which is known to mediate several key aspects of number processing, has been shown to be structurally impaired in fetal alcohol spectrum disorders (FASD), effects on functional activity in this region during number processing have not previously been investigated. This fMRI study of 49 children examined differences in activation associated with prenatal alcohol exposure in five key parietal regions involved in number processing, using tasks involving simple addition and magnitude comparison. Despite generally similar behavioral performance, in both tasks greater prenatal alcohol exposure was related to less activation in an anterior section of the right horizontal intraparietal sulcus known to mediate mental representation and manipulation of quantity. Children with fetal alcohol syndrome and partial fetal alcohol syndrome appeared to compensate for this deficit by increased activation of the angular gyrus during the magnitude comparison task.

Spatial coding of object typical size: evidence for a SNARC-like effect.

The present study aimed to assess whether the representation of the typical size of objects can interact with response position codes in two-choice bimanual tasks, and give rise to a SNARC-like effect (faster responses when the representation of the typical size of the object to which the target stimulus refers corresponds to response side). Participants performed either a magnitude comparison task (in which they were required to judge whether the target was smaller or larger than a reference stimulus; Experiment 1) or a semantic decision task (in which they had to classify the target as belonging to either the category of living or non-living entities; Experiment 2). Target stimuli were pictures or written words referring to either typically large and small animals or inanimate objects. In both tasks, participants responded by pressing a left- or right-side button. Results showed that, regardless of the to-be-performed task (magnitude comparison or semantic decision) and stimulus format (picture or word), left responses were faster when the target represented typically small-sized entities, whereas right responses were faster for typically large-sized entities. These results provide evidence that the information about the typical size of objects is activated even if it is not requested by the task, and are consistent with the idea that objects' typical size is automatically spatially coded, as has been proposed to occur for number magnitudes. In this representation, small objects would be on the left and large objects would be on the right. Alternative interpretations of these results are also discussed.

Further Evidence for a Spatial-Numerical Association in Children Before Formal Schooling

Given the robust finding that number and space are associated systematically at least in school children and adults, it has been concluded that this association might be based on the frequent practice of reading or writing skills, which are usually consolidated by formal schooling. However, first studies contradict this assumption demonstrating that associations of "small" magnitudes with left space and of "large" magnitudes with right space exist already in preschoolers. The present study used a non-symbolic magnitude comparison task to examine whether kindergartners who have not yet been formally instructed in reading and writing show a SNARC effect, that is, whether they would respond more rapidly with the right hand to larger numbers and with the left hand to smaller numbers. This assumption was confirmed by the data. In view of further evidence for an association between number and space that evolves before children are proficient in reading and writing, the role of potential alternative culture-specific, individual, and universal foundations of this association is emphasized and discussed.